[I}
It is to be hoped that when Hersh teaches
mathematics that
(A) when giving solutions to homework problems
he calls them "today's solutions",
(B) he warns the students that there might
be a double penalty for late work, one
for lateness, the other because answers
right when the work is due might be wrong
later,
(C) he gives solace to students who
give lots of wrong answers that they might
be the avant garde of tomorrow's mathematics.
[There was a wonderful mathematician/
piano-playing satirist in the 50's-'70's
whose name I forget (?) (Plagerize, let nothing
evade your eyes, etc.) one of whose
pieces made fun of hippy-counter-culture,
free university mathematics. . .]
[II] Hume????
It is odd that on the one
hand what is important about Hersh is his
insistance on philosophers paying attention
to real historical, working mathematics
but he cites (for support) philosophers who
had little
understanding of such mathematics (Hume)!
What force is citing HUME supposed to
have? If I recall, Hersh cites Hume's Treatise.
Hume himself realized he'd made a terrible
faux pas and restored a bit of mathematics
in the Essay.
In any case: What if I said Locke! or
Leibniz! both of whom saw that there were definitely
right or defintely wrong answers in mathematics.
Surely by Hersh's own criterion Hume must be
evaluated against his understanding of mathematics?
[III] Hersh seems fond of JSMill. Is this wise?
Mill was anti-Humanist, and
Mill's System of Logic had one aim: to not only
remove mathematics as paradigm Scientia (Episteme),
but to reduce all science to such a low level that
what we'd now call social science could count
as a science. And there was a
political-economic agenda here (both Mill and his
father worked for the East India Company). An
even half-heartedly close reading of ON LIBERTY
reveals that most applies only to English
Gentlemen. The Indians were not thought to have
a right to "free speech", for example,
because they were too excitable. The last
is supposed to be an empirical, inductively
established fact. Mill was not a Humanist!!!!
That is, he did not think that "being human"
confers on one any special moral/political
status. Only by empirical, sociological studies
could one determine how much freedom and
responsibility a people could handle? Should
women have the vote? Only if they prove themselves
as capable of being steady and responsible as
gentlmen.
[IV] That someone gives a book a good review does not mean
that they think that its contents are right. It could
very well mean that the book is important in some respect,
as for example, Hersh's is for taking to a popular
audience the thought that philosophers have been guilty of
not paying much attention to real, working mathematics, and
that they ought to do so, albeit Hersh is guilty of a fondness
for philosophers who seem by his lights to support his view
but who have not themselves paid close attention to
real historical working mathematics.
rbrt trgssr